By using the notion of contraction of Lie groups, we transfer L(p)-L(2) estimates for joint spectral projectors from the unit complex sphere S(2n+1) in C(n+1) to the reduced Heisenberg group h(n). In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on h(n). As a consequence, we prove, in the spirit of Sogge's work, a discrete restriction theorem for the sub-Laplacian L on h(n).
Transferring L^p eigenfunction bounds from S^(2n+1) to h^n
CASARINO, VALENTINA;CIATTI, PAOLO
2009
Abstract
By using the notion of contraction of Lie groups, we transfer L(p)-L(2) estimates for joint spectral projectors from the unit complex sphere S(2n+1) in C(n+1) to the reduced Heisenberg group h(n). In particular, we deduce some estimates recently obtained by H. Koch and F. Ricci on h(n). As a consequence, we prove, in the spirit of Sogge's work, a discrete restriction theorem for the sub-Laplacian L on h(n).
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